Final answer:
Article III, Section 1 of the Constitution establishes the Supreme Court and grants it all judicial power, creating the federal court system which is essential for ensuring the separation of powers and a system of checks and balances.
Step-by-step explanation:
Primary Function of Article III, Section 1
The primary function of Article III, Section 1 of the United States Constitution is to establish the Supreme Court as the highest court in the land and to grant it "all judicial power of the United States." This section also authorizes the creation of inferior courts to the Supreme Court, which we refer to as the federal court system. The establishment of these courts is significant for the Constitutional process because it sets up the judicial branch of the government, ensuring a separation of powers and a system of checks and balances.
Furthermore, Section 1 is critical for outlining the purview of the judicial branch and declaring its role in interpreting the law, thus shaping the federal judiciary's structure and functioning. The importance of this section cannot be overstated as it is foundational for upholding the rule of law and providing a mechanism for resolving disputes under federal law and the Constitution.